Method for estimating the signal-to-noise ratio for packet transmission and reception systems of signals based on m-dpsk modulations and apparatus thereof

ABSTRACT

A method of estimating a signal-to-noise ratio from a received M-DPSK modulated signal, comprising a sequence of N known symbols, based on a division of the known symbols N and of N samples of the received signal at the output of the channel into a number of blocks B of length L with B greater than one.

BACKGROUND

1. Technical Field

The present disclosure relates to a method for estimating thesignal-to-noise ratio for packet transmission and reception systems ofsignals based on M-ary differential phase shift keying (M-DPSK)modulations, for example for systems based on receivers of thenon-coherent type with differential demodulator, and an apparatusthereof.

2. Description of the Related Art

In the present communication systems using adaptive modulations forensuring a certain quality of service (QoS), maximizing the spectralefficiency may be advantageous. The key idea of the adaptive modulationis reacting to the changes of the channel conditions by using strongmodulation schemes in the case of bad channel conditions and employingless strong modulation schemes in the case of good channel conditionsfor increasing the transmission speed. The adaptive modulations may beemployed both in single carrier systems and in multiple carrier systems,in both cases a reliable estimation of the channel conditions is needed,for example an estimation of the signal-to-noise ratio (SNR), in orderto choose the modulation to be employed.

The apparatuses for estimating the signal-to-noise ratio or SNRestimators may be divided in two categories: “data aided” estimators and“not data aided” estimators i.e., the estimators acting on a known datasequence and those acting on an unknown data sequence. The present dataaided SNR estimators applied to non-coherent receivers at the input of adifferential demodulator do not allow good estimations of thesignal-to-noise ratio to be obtained in the presence of impairments thatcause a progressive phase shifting of the received constellationsymbols. An example of such impairments is the presence of frequencyoffsets, between transmitter and receiver, on the carrier frequency. Onthe other hand, the present data aided SNR estimators applied tonon-coherent receivers at the output of a differential demodulator arestronger against those impairments, such as carrier frequency offsets,but more sensitive to the noise.

BRIEF SUMMARY

In an embodiment a method is provided for estimating the signal-to-noiseratio for packet transmission and reception systems of signals based onM-DPSK modulations which allows good estimation values to be obtainedeven in the presence of impairments that cause a progressive phaseshifting of the received constellation symbols. An example of suchimpairments is the presence of carrier frequency offsets.

In an embodiment, a method for estimating the signal-to-noise ratio fora packet transmission and reception system of signals having a knownsequence with M-DPSK modulation with at least one carrier, said systemcomprising the packet transmission of the signal with the sequence of Nknown symbols, N being a positive integer number, said transmissioncomprising a M-DPSK modulation of the signal to be transmitted by meansof a M-PSK mapper and a differential block, the transmission of theM-DPSK modulated signal through a channel having a constant gain overall the N symbols and in the presence of noise with null average, andthe reception of the signal at the output of the channel, comprises theestimation of the signal-to-noise ratio from the N samples (r_(k)) ofthe received signal (r(t)), comprising the sequence of known N symbols,and from the known N transmitted symbols (a_(k)) both divided into Bblocks of L length, with B and L being positive integer numbers, and Bgreater than one, and the calculation of the estimation of thesignal-to-noise ratio by means of the equation:

$\begin{matrix}{{SNR} = {{( {1 - \frac{1}{L}} )\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}} - \frac{1}{L}}} \\{= {\frac{( {L - 1} ){\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}} - {L{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}}\end{matrix}$

where l_(b)=L·b+l, l is the index denoting the position of the firstknown symbol of the sequence of length N in the packet, r_(k) is thesample of the received signal at the output of the channel correspondentto the known transmitted symbol, a_(k) is the M-DPSK known transmittedsymbol, a_(k) is the complex conjugate of the M-DPSK known transmittedsymbol and SNR indicates the estimation of the signal-to-noise ratio.

In an embodiment, if the length L of the B blocks is sufficiently greatto average the noise, said estimation of the signal-to-noise ratio isgiven by:

${SNR} = {\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}.}$

For example, in an embodiment when the length L is greater than athreshold, the signal-to-noise ratio may be estimated using the aboveequation.

In an embodiment, the B blocks are expressed by

$B = {{\frac{N - L}{L - O} + 1} \geq \frac{N}{L}}$

wherein O indicates the overlapping factor of consecutive blocks havinglength L, said estimation of the signal-to-noise ratio being given by:

${SNR} = {\frac{\frac{( {L - 1} )}{B \cdot L}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - {\frac{1}{L}.}}$

In an embodiment, the transmission and reception system is of thepass-band type and the reception is of the non-coherent type withdifferential demodulation, the estimation of the signal-to-noise ratiois effectuated before the differential demodulation of the signal.

In an embodiment, the transmission and reception system is of themultiple carrier type.

In an embodiment, an apparatus for estimating the signal-to-noise ratiofor a packet transmission and reception system of signals having a knowndata sequence by means of a M-DPSK modulation with at least one carrier,said system comprising means for the packet transmission of the signalwith the sequence of N known symbols, with N positive integer number,said transmission means comprising a M-DPSK modulator of the signal totransmit comprising a M-PSK mapper and a differential block, said M-DPSKmodulated signal being adapted to pass through a channel having constantgain over all the N symbols and in presence of noise with null average,said system comprises means for receiving the signal at the output ofthe channel, said apparatus comprising first means adapted to divide theN known symbols (a_(k)) and N samples (r_(k)) of the received signal (r(t)) into B blocks of L length with B and L positive integer numbers,and B greater than one, and second means adapted to calculate theestimation of the signal-to-noise ratio by means of the equation:

$\begin{matrix}{{SNR} = {{( {1 - \frac{1}{L}} )\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}} - \frac{1}{L}}} \\{= {\frac{( {L - 1} ){\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}} - {L{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}}\end{matrix}$

wherein l_(b)=L·b+l, l is the index denoting the position of the firstknown symbol of the sequence of length N in the packet, r_(k) is thesample of the received signal at the output of the channel correspondentto the known transmitted symbol, a_(k) is the M-DPSK known transmittedsymbol, a*_(k) is the complex conjugate of the M-DPSK known transmittedsymbol and SNR indicates the estimation of the signal-to-noise ratio.

In an embodiment, if the length L of the blocks B is sufficient great toaverage the noise said second means are adapted to calculate theestimation of the signal-to-noise ratio by the equation:

${SNR} = \frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}$

In an embodiment, the first means are adapted to overlap consecutiveblocks having length L of a factor O, said B blocks being expressed by

$B = {{\frac{N - L}{L - O} + 1} \geq \frac{N}{L}}$

wherein O indicates the overlapping factor of consecutive blocks havinglength L, said second means being adapted to effectuate the estimationof the signal-to-noise ratio by the equation:

${SNR} = {\frac{\frac{( {L - 1} )}{B \cdot L}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - {\frac{1}{L}.}}$

In an embodiment, the transmission and reception system is of thepass-band type, said reception means of the signal effectuating anon-coherent reception and comprising a differential demodulator, saidestimation apparatus being adapted to calculate the estimation ofsignal-to-noise ratio of the signal at the input of the differentialdemodulator.

In an embodiment, the transmission and reception system is of themultiple carrier type.

In an embodiment, a packet transmission and reception system of signalshaving a known data sequence by means of a M-DPSK modulation with atleast one carrier, said system comprising means for the packettransmission of the signal with the sequence of N known symbols, with Npositive integer number, said transmission means comprising a M-DPSKmodulator of the signal to transmit comprising a M-PSK mapper and adifferential block, said M-DPSK modulated signal being adapted to passthrough a channel having constant gain over all the N symbols and inpresence of noise with null average, said system comprising means forreceiving the signal at the output of the channel which comprises adifferential demodulator, characterized by comprising an apparatus toeffectuate the estimation of the signal-to-noise ratio of the signal atthe input of said differential demodulator.

In an embodiment, a method comprises: receiving a modulated signal, thesignal comprising a sequence of N known symbols modulated using M-aryDifferential Phase Shift Keying (M-DPSK) modulation with at least onecarrier; and estimating, using at least one processor, a signal-to-noiseratio of the received modulated signal based on a division of the Nknown symbols (a_(k)) and of N samples (r_(k)) of the received signal(r(t)) into a number of blocks B of a length L, with N, B and L beingpositive integer values and B greater than one.

In an embodiment, the estimation of the signal-to-noise ratio based onthe number of blocks B and the length L comprises estimating thesignal-to-noise ratio based on the complex conjugate of the M-DPSKmodulated known symbols.

In an embodiment, the estimation of the signal-to-noise ratio based onthe number of blocks B and the length L, and B greater than one, isperformed according to:

$\begin{matrix}{{SNR} = {{( {1 - \frac{1}{L}} )\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}\; {r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}}} - \frac{1}{L}}} \\{= {\frac{( {L - 1} ){\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}{{\sum\limits_{k = l}^{l + N - 1}\; {r_{k}}^{2}} - {L{\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}}\end{matrix}$

wherein l_(b)=L·b+l, l is the index denoting the position of the firstknown symbol of the sequence of length N in the packet, r_(k) is thesample of the received signal at the output of the channel correspondentto the known transmitted symbol, a_(k) is the M-DPSK known transmittedsymbol, a*_(k) is the complex conjugate of the M-DPSK known transmittedsymbol and SNR indicates the estimation of the signal-to-noise ratio.

In an embodiment, when the length L of the blocks B is greater than athreshold, the estimation of the signal-to-noise ratio is given by:

${{SNR} = \frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}\; {r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}}},$

wherein l_(b)=L·b+l, l is the index denoting the position of the firstknown symbol of the sequence of length N in the packet, r_(k) is thesample of the received signal at the output of the channel correspondentto the known transmitted symbol, a_(k) is the M-DPSK known transmittedsymbol, a*_(k) is the complex conjugate of the M-DPSK known transmittedsymbol and SNR indicates the estimation of the signal-to-noise ratio.

In an embodiment,

$B = {{\frac{N - L}{L - O} + 1} \geq \frac{N}{L}}$

wherein O indicates an overlapping factor of consecutive blocks havinglength L, and estimation of the signal-to-noise ratio being given by:

${{SNR} = {\frac{\frac{( {L - 1} )}{B \cdot L}\; {\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}\; {\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}},$

wherein l_(b)=L·b+l, l is the index denoting the position of the firstknown symbol of the sequence of length N in the packet, r_(k) is thesample of the received signal at the output of the channel correspondentto the known transmitted symbol, a_(k) is the M-DPSK known transmittedsymbol, a*_(k) is the complex conjugate of the M-DPSK known transmittedsymbol and SNR indicates the estimation of the signal-to-noise ratio.

In an embodiment, the method further comprises: filtering the receivedmodulated signal; and applying non-coherent type differentialdemodulation to the filtered signal after estimation of thesignal-to-noise ratio. In an embodiment, the at least one carriercomprises multiple carriers.

In an embodiment, an apparatus comprises: a module configured to obtaina number B of blocks of a length L based on a division of a number N ofknown symbols, and of a number N of samples of the received signal atthe output of the channel with N, B and L being positive integer values,and B greater than one; and an estimator configured to estimate, basedon the number of blocks B and the length L, a signal-to-noise ratio of areceived signal comprising the sequence of the N known symbols modulatedusing M-ary Differential Phase Shift Keying (M-DPSK) modulation with atleast one carrier signal.

In an embodiment, the module configured to obtain the number of blocks Bcomprises a divider configured to divide the N known symbols and Nsamples of the received signal into the number of blocks B of the lengthL, and B greater than one.

In an embodiment, the estimator is configured to estimate thesignal-to-noise according to:

$\begin{matrix}{{SNR} = {{( {1 - \frac{1}{L}} )\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}\; {r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}}} - \frac{1}{L}}} \\{= {\frac{( {L - 1} ){\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}{{\sum\limits_{k = l}^{l + N - 1}\; {r_{k}}^{2}} - {L{\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}}\end{matrix}$

wherein l_(b)=L·b+l, l is the index denoting the position of the firstknown symbol of the sequence of length N in the packet, r_(k) is thesample of the received signal at the output of the channel correspondentto the known transmitted symbol, a_(k) is the M-DPSK known transmittedsymbol, a*_(k) is the complex conjugate of the M-DPSK known transmittedsymbol and SNR indicates the estimation of the signal-to-noise ratio.

In an embodiment, if the length L of the blocks B is greater than athreshold, the estimator is configured to estimate the signal-to-noiseratio according to

${{SNR} = \frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}\; {r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}\; {{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}\; {r_{k}a_{k}^{*}}}}}^{2}}}}},$

wherein l_(b)=L·b+l, l is the index denoting the position of the firstknown symbol of the sequence of length N in the packet, r_(k) is thesample of the received signal at the output of the channel correspondentto the known transmitted symbol, a_(k) is the M-DPSK known transmittedsymbol, a*_(k) is the complex conjugate of the M-DPSK known transmittedsymbol and SNR indicates the estimation of the signal-to-noise ratio.

In an embodiment, the apparatus further comprises: a filter configuredto filter the received signal; and a differential demodulator configuredto demodulate the received signal and to receive as an input theestimated signal-to-noise ratio. In an embodiment, the at least onecarrier signal comprises a plurality of carrier signals.

In an embodiment, a computer-readable memory medium's contents cause atleast one processor to perform a method, the method comprising:obtaining a number of blocks B of a length L based on a division of anumber of known symbols N and of a number N of samples of the receivedsignal at the output of the channel into the number of blocks B oflength L, with B, L and N positive integer values, and B greater thanone; and estimating, based on the number of blocks B and the length L, asignal-to-noise ratio of a received signal comprising a sequence of theN known symbols modulated using M-ary Differential Phase Shift Keying(M-DPSK) modulation with at least one carrier signal. In an embodiment,the method further comprises differential demodulation of the receivedsignal.

In an embodiment, the obtaining comprises dividing the N known symbolsand N samples of the received signal at the output of the channel intothe number of blocks B of length L, and B greater than one. In anembodiment, B is greater than N divided by L.

In an embodiment, a system comprises: a differential demodulatorconfigured to demodulate a received signal comprising a sequence of Nknown symbols modulated using M-ary Differential Phase Shift Keying(M-DPSK) modulation with at least one carrier signal; and an estimatorconfigured to estimate a signal-to-noise ratio of the received signalbased on a division of the N known symbols and of N samples of thereceived signal at the output of the channel into a number of blocks Bof length L, with N, B and L being positive integer values, and Bgreater than one.

In an embodiment, the estimator comprises a divider configured to dividethe known symbols N and N samples of the received signal at the outputof the channel into the number of blocks B of the length L, and Bgreater than one.

In an embodiment, the system further comprises a filter.

In an embodiment, the system further comprises a transmitter configuredto transmit a signal, wherein the differential demodulator and theestimator are configured to receive the transmitted signal. In anembodiment, the system further comprises a transmitter configured totransmit modulated signals.

In an embodiment, a system comprises: means for obtaining a number ofblocks B of a length L based on a division of a sequence of knownsymbols N and of N samples of the received signal at the output of thechannel into the number of blocks B; and means for estimating, based onthe number of blocks B and the length L, a signal-to-noise ratio of areceived signal comprising a sequence of the N known symbols modulatedusing M-ary Differential Phase Shift Keying (M-DPSK) modulation with atleast one carrier signal.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The features and advantages of embodiments will be apparent from thefollowing detailed description of a practical embodiment thereof, shownby way of non-limiting example in the accompanying drawings, in which:

FIG. 1 is the equivalent base-band scheme of a pass-band packettransmission and reception system of the single carrier type with anM-DPSK modulator and demodulator and apparatus for estimating thesignal-to-noise ratio according to an embodiment;

FIG. 2 is a graph of the estimated signal-to-noise ratio SNRs versus theexact value SNRe of an SNR estimator in accordance with the known art.

FIG. 3 is a graph of the mean square error MSE versus the exact value ofthe signal-to-noise ratio SNRe of the estimator in accordance with theknown art.

FIG. 4 is a graph of the estimated signal-to-noise ratio SNRs versus theexact value SNRe of the SNR estimator in accordance with an embodiment.

FIG. 5 is a graph of the mean square error MSE versus the value of thesignal-to-noise ratio SNRe of the estimator in accordance with anembodiment.

FIG. 6 is a graph of the estimated signal-to-noise ratio SNRs versus theexact value SNRe of the SNR estimator in accordance with two embodimentsfor some combinations of B and L.

FIG. 7 is a graph of the mean square error MSE versus the value of thesignal-to-noise ratio SNRe of the SNR estimator in accordance with twoembodiments for some combinations of B and L.

FIG. 8 is a graph of the estimated signal-to-noise ratio SNRs versus theexact value SNRe of the SNR estimator in accordance with an embodimentfor some combinations of B and L and O.

FIG. 9 is a graph of the mean square error MSE versus the value of thesignal-to-noise ratio SNRe of the SNR estimator in accordance with anembodiment for some combinations of B and L and O.

FIG. 10 is the equivalent base-band scheme of a pass-band packettransmission and reception multiple carrier system with M-DPSK modulatorand demodulator and apparatus for estimating the signal-to-noise ratioin accordance with an embodiment.

FIG. 11 is a graph of the estimated signal-to-noise ratio SNRs versusthe exact value SNRe of the SNR estimator in accordance with anembodiment for a multiple carrier transmission and reception system.

FIG. 12 is a graph of the mean square error MSE versus the value of thesignal-to-noise ratio SNRe of the SNR estimator in accordance with anembodiment for a multiple carrier transmission and reception system.

DETAILED DESCRIPTION

In the following description, numerous specific details are given toprovide a thorough understanding of the embodiments. The embodiments canbe practiced without one or more of the specific details, or with othermethods, components, materials, etc. In other instances, well-knownstructures, materials, or operations are not shown or described indetail to avoid obscuring aspects of the embodiments.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure, orcharacteristic described in connection with the embodiment is includedin at least one embodiment. Thus, the appearances of the phrases “in oneembodiment” “according to an embodiment” or “in an embodiment” andsimilar phrases in various places throughout this specification are notnecessarily all referring to the same embodiment. Furthermore, theparticular features, structures, or characteristics may be combined inany suitable manner in one or more embodiments.

The headings provided herein are for convenience only and do notinterpret the scope or meaning of the embodiments.

FIG. 1 shows the equivalent base-band scheme of a pass-band packettransmission and reception system 1000 of signals with a single carrier.The M-DPSK modulator 1 comprises an M-PSK bit mapper 2 where M is themodulation order, i.e., the number of possible constellation symbols.The mapper may comprise a serial-to-parallel converter followed by a maptransforming a sequence of log₂M bits c_(i) into correspondingconstellation points with values a_(k) where:

${a_{k}^{\prime} = {^{{j\phi}_{k}} = ^{j\frac{2\pi}{M}k}}},{k = 0},\ldots \mspace{14mu},{M - 1}$

and the modulation symbol period T is given by T=T_(c) log₂ M whereT_(c) is the information bit period. In the bit mapper comprising theM-PSK mapper 2 and the differential block 3, the phase δ_(k) associatedwith the symbol transmitted at the kT instant is the phase transmittedat the preceding instant (k−1)T, i.e., δ_(k−1), with a phase increaseφ_(k) which may assume one of the M values belonging to the range [0,2π/M, . . . , 2π(M−1)/M]. Therefore, in the M-PSK bit mapper, the phasetransmitted at the kT instant is given by: δ_(k)=δ_(k−1)+φ_(k). Themodulated symbol at the output of the differential block 3 isa_(k)=e^(jδk). The receiver retrieves the transmitted data using thephase difference between consecutive samples without needing to retrievethe phase offset introduced by the channel and the phase offset betweentransmitter and receiver on the carrier frequency.

The symbol a_(k) is associated with a limited-band h_(T) (t) filter 4 sothat at the output of filter 4 there is the signal

${s(t)} = {\sum\limits_{i = {- \infty}}^{+ \infty}\; {a_{i}{h_{T}( {t - {i\; T}} )}}}$

where the index k has been replaced by the index i; said signal is atthe input of the transmission channel 5.

Assuming that the transmission channel 5 is a channel which is flat onthe signal band and time-invariant with a constant gain

g _(ch)(t)=G,

the signal at the output of the channel 5 still has a PSK structure;noise is added to the signal s(t), preferably an additive white Gaussiannoise w(t) (AWGN) having a null average with double-sided spectral powerdensity of

N₀/2

Indicating the convolution by the symbol

, and the frequency and phase offset on the carrier frequency betweenthe transmitter and the receiver by Δf and Δθ, the signal x(t) at theoutput of the channel 5 and at the input of the receiver 10 is given by:

x(t)=(s

g _(ch)(t)+w(t))·e ^(j(2πΔf t+Δθ)) G·s(t)·e ^((2πΔft+Δθ)) {tilde over(w)}(t),

where

{tilde over (w)}(t)=w(t)·e ^(j(2πΔft+Δθ)).

Assuming that the frequency offset Δf is sufficiently small andconsidering the filter 6 of the receiver with a function h_(R)(t) at theoutput of the filter, the following equation is given

${{r(t)} = {{x \otimes {h_{R}(t)}} \cong {{^{j{({{2{\pi\Delta}\; {ft}} + {\Delta\vartheta}})}}{\sum\limits_{i = {- \infty}}^{+ \infty}\; {a_{i}{h( {t - {i\; T}} )}}}} + {n(t)}}}},{where}$${h(t)} = {{{G \cdot ( {h_{T} \otimes {h_{R}(t)}} )}{\mspace{11mu} \;}{and}\mspace{14mu} {n(t)}} = {\overset{\sim}{w} \otimes {{h_{R}(t)}.}}}$

At the sampling instant kT+t₀ where t₀ is the sampling phase thefollowing equation is given

${r_{k} = {{G \cdot ( {^{j{\lbrack{{2{\pi\Delta}\; {f({{kT} + t_{0}})}} + {\Delta\vartheta}}\rbrack}}{\sum\limits_{i = {- \infty}}^{+ \infty}\; {a_{i}h_{k - i}}}} )} + n_{k}}},{where}$r_(k) = r(kT + t₀), h_(k) = h(kT + t₀)  and   n_(k) = n(kT + t₀).

Assuming that the function h_(k)=h(kT+t₀) satisfies the Nyquistcondition:

$h_{k - i} = \{ \begin{matrix}1 & {{{if}\mspace{14mu} k} = i} \\0 & {{{if}\mspace{14mu} k} \neq i}\end{matrix} $

the following equation is given

r _(k) =G·a _(k) e ^(j[2πΔf(kT+t) ₀ ^()+Δθ]) +n _(k) =G·a _(k) e^(j[2πΔfkT+Δφ]) n _(k),

where Δφ=2πΔft₀+Δθ.

The sampled signal r_(k) is processed by a M-DPSK differentialdemodulator module 7 and sent to an inverted bit mapper 8 providingdecisions on the received bits q_(i).

The demodulator multiplies the sampled signal r_(k) by its delayed andconjugated version r*_(k−1), where the symbol * indicates the complexconjugate, providing the sample Z_(k) given by:

$\begin{matrix}{z_{k} = {r_{k} \cdot r_{k - 1}^{*}}} \\{= {( {{{G \cdot a_{k}}^{j{({{2{\pi\Delta}\; {fkT}} + {\Delta\varphi}})}}} + n_{k}} )( {{{G^{*} \cdot a_{k - 1}^{*}}^{- {j{({{2{\pi\Delta}\; {f({k - 1})}T} + {\Delta\varphi}})}}}} + n_{k - 1}^{*}} )}} \\{= {{{G}^{2}a_{k}a_{k - 1}^{*}^{{j2\pi\Delta}\; {fT}}} + {n_{k} \cdot n_{k - 1}^{*}} + {{G \cdot a_{k}}{^{j{({{2{\pi\Delta}\; {fkT}} + {\Delta\varphi}})}} \cdot}}}} \\{{n_{k - 1}^{*} + {{G^{*} \cdot a_{k - 1}^{*}}{^{- {j{({{2{\pi\Delta}\; {f({k - 1})}T} + {\Delta\varphi}})}}} \cdot n_{k}}}}}\end{matrix}$

where the normalized frequency offset is defined as Δf_(n)=Δf·T.

The useful term i.e., the term |G|² a_(k)a*_(k−1)e^(j2πΔfT) isinsensitive to the phase offset and, if Δf_(n) is sufficiently small,the frequency offset may be neglected.

A disadvantage of some such differential demodulators is due to the factthat the term bonded to the noise is amplified. In order to avoid saiddisadvantage, the SNR estimators may act on the signal r(t) at the inputof the M-DPSK block 7 of the receiver.

Considering an N sequence of samples r_(k) consecutively received and las the index denoting the position of the first known symbol of thesequence in the packet, assuming the channel gain G to be constant overthe N samples and the number N to be sufficiently great so as to averageout the noise, assumed as a null average, and that |a_(k) ²=1 forunitary power PSK constellations, the following equation is given:

${\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}\; {r_{k}}^{2}}} \cong {{\hat{G}}^{2} + {\hat{\sigma}}_{n}^{2}}$

where the values Ĝ and {circumflex over (σ)}_(n) ² denote the channelestimation and the noise variance estimation, respectively. Assuming tohave N available known symbols at the beginning of the usefultransmission and an N sufficiently great, for example greater than 8 andin some embodiments equal to 32, such as to allow the noise, assumed asa null average, to be averaged out, the following equation is given:

${{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}\; {r_{k}a_{k}^{*}}}}}^{2} \cong {{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}\; {G \cdot ^{j{({{2{\pi\Delta}\; {fkT}} + {\Delta\varphi}})}}}}}}^{2}$

and assuming the channel gain to be constant over all the N symbols andthe frequency offset Δf_(n) to be negligible, i.e.,Δf_(n)l≈Δf_(n)(l+N−1), the following equation is given:

${{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}\; {r_{k}a_{k}^{*}}}}}^{2} \cong {\hat{G}}^{2}$

representing the estimation of the squared channel gain.

The estimation of the signal-to-noise ratio SNR is determined by:

${SNR} = \frac{{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}a_{k}^{*}}}}}^{2}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}a_{k}^{*}}}}}^{2}}$

In the presence of frequency offsets Δf_(n), when the conditionΔf_(n)l≈Δf_(n)(l+N−1) is no longer true and therefore the approximation

${{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}a_{k}^{*}}}}}^{2} \cong {\hat{G}}^{2}$

is no longer satisfied, the SNR estimation, indicated as SNV, degradesas shown in the graphs of FIGS. 2 and 3 relating to the estimatedsignal-to-noise ratio SNRs versus the exact value SNRe over variousvalues of Δf_(n) and to the mean square error MSE against the value SNReover various values of Δf_(n), respectively. As the frequency offsetΔf_(n) increases, the MSE error is noted to dramatically increase andthe values of SNRs diverge from SNRe. In an embodiment, the N knownsymbols a_(k) and the N samples r_(k) consecutively received andcorresponding to the known symbols a_(k) are divided into B blocks oflength L, N=B·L, i.e., the known sequence N and the N received samplesnow consist of B blocks of length L, with B greater than one. Estimator100 comprises a divider module 101 allowing the N known symbols a_(k)and the N samples r_(k) consecutively received and corresponding to theknown symbols a_(k) to be converted into B blocks of length L. Thefollowing equation is given:

${\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}=={\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{G\; ^{j{({{2\pi \; \Delta \; {fkT}} + {\Delta\varphi}})}}}}} + {\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{n_{k}a_{k}^{*}}}}}}^{2}}}$

where l_(b)=L·b+l. Assuming the channel gain G to be constant over the Lsamples and the number L to be sufficiently great, for example, greaterthan 8, so as to allow the noise, assumed as a null average, to beaveraged out, and the condition

Δf _(n) l _(b) ≈Δf _(n)(l _(b) +L−1)

to be satisfied, the following approximation may be carried out:

${\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}} \cong {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{G_{l_{b}}}^{2}}} \cong {\hat{G}}^{2}$

The SNR estimator 100 comprises a SNR calculation block 102 configuredto calculate the estimated signal-to noise ratio. For example, theestimated SNR may be calculated by the following equation:

${SNR} = \frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}$

FIG. 4 shows a graph of the estimated signal-to noise ratio SNRs versusthe exact value SNRe over values of Δf_(n) being 10⁻³ and 2·10⁻³ withB=2 and L=16 of the SNR estimator 100, indicated as SNVS(B, L), inaccordance with an embodiment, whereas FIG. 5 shows a graph of the meansquare error MSE against the value SNRe over values of Δf_(n) being 10⁻³and 2·10⁻³ with B=2 and L=16 of the SNR estimator in accordance with anembodiment; both graphs show an estimator in accordance with the knownart for Δf_(n)=0, indicated as BOUND. From the values of FIGS. 2, 3 andFIGS. 4, 5, the improvement of the performances of the SNR estimator inaccordance with an embodiment is apparent as compared to the estimatorin accordance with the known art.

In accordance with another embodiment, assuming similarly to the aboveembodiment the channel gain G to be constant over the L samples and thecondition Δf_(n)l_(b)≈Δf_(n)(l_(b)+L−1) to be satisfied, and assumingthe number L, differently from

the first embodiment, not to be sufficiently great to average the noiseout, and with B>1, the following approximation may be carried out:

${\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}} \cong {{\hat{G}}^{2} + \frac{\sigma_{n}^{2}}{L}}$

and therefore the expression of the signal-to-noise ratio SNR calculatedfrom the block 102 of the estimator 100 may use the following equation:

$\begin{matrix}\begin{matrix}{{SNR} = {{( {1 - \frac{1}{L}} )\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}} - \frac{1}{L}}} \\{= {\frac{( {L - 1} ){\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}} - {L{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}}\end{matrix} & \;\end{matrix}$

The SNR ratio comprises a weighting factor 1−1/L to weight thesignal-to-noise ratio and a corrective term −1/L, it is noted that, if Lis sufficiently great, the weighting factor (1−1/L) and the correctiveterm −1/L may be ignored, thus recovering the equation of the embodimentof the estimator discussed above. In some cases, the corrective term−1/L alone may be ignored.

From the equations relating to the signal-to-noise ratio SNR of theabove described embodiments, it is apparent that for greater values of Bthe estimator is stronger with respect to the frequency offsets whereasfor low values of L the estimator is more sensitive to the noise.

FIG. 6 shows a graph of the estimated signal-to noise ratio SNRs versusthe exact value SNRe over values of Δf_(n) being 2·10⁻³ with values of Bbeing 2, 4, 8 and respective values of L being 16, 8, 4 of the SNRestimator in accordance with the above described embodiments, whereasFIG. 7 shows a graph of the mean square error MSE versus the value SNReover values of Δf_(n) being 2·10⁻³ with values of B being 2, 4, 8 andrespective values of L being 16, 8, 4 of the SNR estimator 100 inaccordance with the first and second described embodiments; theestimator in accordance with the first described embodiment is indicatedas SNVS(B, L), whereas that in accordance with the second describedembodiment is indicated as RSNVS(B, L). From the values of FIGS. 6 and7, the improvement of the RSNVS estimator performances is apparent ascompared to the SNVS with low values of L.

In a third described embodiment, the divider block 101 of the SNRestimator 100, in addition to the division N=B·L, also allows to overlapconsecutive blocks having a length L of a factor O with B>1. Given aknown sequence having a length N, the number of possible divisions isgiven by

$B = {{\frac{N - L}{L - O} + 1} \geq {\frac{N}{L}.}}$

Defining l_(b)=(L−O)·b+l, the SNR estimator 100 in accordance with anembodiment is configured to calculate the signal-to-noise ratio to becalculated with the block 102 using the following equation:

${SNR} = \frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}$

In accordance with a fourth described embodiment, considered as avariant of the third embodiment, the block 102 of the estimator 100comprises, similarly to the second embodiment, a weighting factor 1−1/Lto weight the signal-to-noise ratio and a corrective term −1/L such thatthe calculation of the signal-to-noise ratio may be performed by thefollowing equation:

${SNR} = {\frac{\frac{L - 1}{B \cdot L}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}$

It is noted that, similarly to the second embodiment, if L issufficiently great, the weighting factor (1−1/L) and the corrective term−1/L may be ignored, thus recovering the equation of the thirdembodiment of the estimator. In some cases, the corrective term −1/Lalone may be ignored.

Once N has been determined, more combinations of B and L may be obtainedwith good performances, as shown in FIGS. 8 and 9 where there are showna graph of the estimated signal-to-noise ratio SNRs versus the exactvalue SNRe over values of Δf_(n) being 2·10⁻³ with values of B being 4,6, 8, 10, 14 and L being 4, 5, 6, 7, 8 and 0 being 2, 4 of the SNRestimator in accordance with the second and fourth describedembodiments, and a graph of the mean square error MSE versus the valueSNRe over values of Δf_(n) being 2·10⁻³ with values of B being 4, 6, 8,10, 14 and L being 4, 5, 6, 7, 8 and O being 2, 4 of the SNR estimatorin accordance with the second and fourth embodiments, respectively, theestimator in accordance with the second embodiment is indicated asRSNVS(B, L) whereas the estimator in accordance with the fourthembodiment is indicated as RSNVSO(O, B, L).

The blocks 101 and 102 of the estimator 100 may comprise amicroprocessor 103 and a memory 104 on which an application software isrunning thus causing the estimator 100 to perform the division N=B·L andin some embodiments also the overlapping of consecutive blocks having alength L of a factor O as previously specified and the execution of thecalculation of the signal-to-noise ratio, for example according to anyone of the preceding equations. In an embodiment, the estimator maycomprise a look-up table for obtaining the number of blocks B of lengthL from the known number of symbols N.

A SNR estimator, for example the SNR 100 in accordance with theembodiments discussed above, may also be used for multiple carriersystems, such as the OFDM (Orthogonal Frequency Division Multiplexing)systems. In these transmission systems, there are multiple phenomenathat may cause a progressive phase shifting of the receivedconstellation, resulting in effects which are completely similar to thecarrier frequency offset in the single carrier systems. It is for thisreason that using the estimator may also be useful in multiple carriersystems, for example at the input of the differential demodulator,rather than the estimator in accordance with the known art. Thephenomena responsible for the phase shifting of the receivedconstellation may include: the carrier frequency offset, the packetsynchronization offset and the sampling frequency offset. Each of thesephenomena produces a different effect over the various subcarriers ofthe system and on the various symbols forming the transmitted packet.For example, the carrier frequency offset, in a pass-band system,produces a phase shifting of the constellation being constant on all thesubcarriers of an OFDM symbol but increasing over time for everyreceived OFDM symbol. On the other hand, the packet synchronizationoffset produces a rotation proportional to the subcarrier index, howeverremaining constant over all the OFDM symbols of the packet. The samplingfrequency offset produces a rotation of the received constellation beingdifferent according to both the subcarrier index and the received OFDMsymbol.

Given the complexity of the phenomenon, in an OFDM system, a “dataaided” SNR estimator may be implemented in different ways, based on thenegative effect to be minimized. An SNR estimator may act on thefrequency in the various carriers or over time between the differenttransmitted OFDM symbols. However, in any case, the known transmittedsequence of length N and the N received samples may be processed using Bblocks of length L in order to reduce the negative effect of therotation of the constellation in estimating the value of SNR. By way ofnon-limiting example, refer to a pass-band OFDM system where everysubcarrier is M-DPSK modulated, i.e., the differential is achieved overtime, and no recovery of the carrier frequency is achieved during thereception; an OFDM system 2000 in accordance with an embodiment is shownin FIG. 10. The M-PSK modulator 200 comprises a serial-to-parallelconverter followed by a map which transforms a sequence of log₂M bitsC_(i) into corresponding constellation points, a′_(l). The M-PSK mapper200 is followed by a serial-to-parallel converter 201 having N_(FFT)outputs with values of a′_(n,k) where n and k represent the index of theOFDM symbol and the index of the subcarrier, respectively, and having aduration of

T·N_(FFT)

where

T=T_(c) log₂ M,

being T_(c) the information bit period. The M-DPSK modulator comprisesN_(FFT) differential blocks 202 configured to output signals a_(n,0), .. . , a_(n,N) _(FFT−1) , being

a _(n,k) =a′ _(n,k) ·a _(n−1,k′)

at the input of a transform block 203 configured to carry out theinverse Fourier transform of said signals and a block 204 configured tocarry out the parallel-to-serial conversion of the signals. The obtainedsignals are at the input of a channel 205 with a transfer function G(f).

OFDM systems, like the OFDM system 2000 of FIG. 10, may allow the signalband to be divided into sub-bands in which the transfer function of thechannel G(f) may be approximated as almost flat. Under these conditions,an estimator may independently be applied to every OFDM subcarrier. Oncethe noise w(t) has been added, the passage through theserial-to-parallel converter 206 and the block for applying the Fouriertransform 207, in the presence of an offset between the carrierfrequency of the transmitter and receiver, the sample relating to then^(th) symbol and the n^(th) subcarrier has the following expression:

$r_{n,h} = {{\sum\limits_{k = o}^{N_{FFT} - 1}{a_{n,k}G_{k}\sin \; {c_{N_{FFT}}( {k + {\Delta \; f\; \frac{N_{FFT}}{F}} - h} )}^{{- j}\; {\pi {({k + {\Delta \; f\; \frac{N_{FFT}}{F}} - h})}}\frac{N_{FFT} - 1}{N_{FFT}}}}} + W_{n,h}}$

where a_(n,k) and G_(k) are the transmitted M-DPSK symbol and thecomplex coefficient of the channel gain on the k^(th) subcarrier,respectively, W_(n,h) represents the noise after the discrete Fouriertransform (DFT), N_(FFT) is the number of subcarriers, F=1/T is thesampling frequency and the function

${\sin \; {c_{N}(x)}} = {\frac{1}{N} \cdot \; \frac{\sin \; \pi \; x}{\sin \; \frac{\pi}{N}x}}$

The preceding relation may be written as:

$r_{n,h} = {{( {a_{n,h}G_{h}\sin \; {c_{N_{FFT}}( {\Delta \; f\; \frac{N_{FFT}}{F}} )}} )^{j\; \pi \; \frac{{\Delta \; f\; N_{FFT}} - 1}{F\mspace{11mu} N_{FFT}}}} + I_{n,h} + W_{n,h}}$where$I_{n,h} = {\sum\limits_{\underset{k \neq h}{k = 0}}^{N_{FFT} - 1}{a_{n,k}G_{k}\sin \; {c_{N_{FFT}}( {k + {\Delta \; f\; \frac{N_{FFT}}{F}} - h} )}^{j\; {\pi {({k + {\Delta \; f\; \frac{N_{FFT}}{F}} - h})}}\frac{N_{FFT} - 1}{N_{FFT}}}}}$

represents the channel interference due to the frequency offset Δf, saidterm degrades the performances of the OFDM systems and makes the SNRestimators 100 more sensitive to the frequency offset as compared tosingle carrier transmission and reception systems. The frequency offsetdetermines a phase rotation for the received symbols being constant overall the subcarriers, said phase rotation is proportional to thenormalized frequency offset Δf_(n) with respect to the samplingfrequency F,

Δf _(n) =Δf/F=Δf·T.

The samples r_(n,0), . . . , r_(n,N) _(FFT−1) are at the input of theSNR estimators 100 and then at the input of the M-DPSK receivers 208,parallel-to-serial converter 209, inverted mapper 210 in order to havethe estimated bits m_(i) corresponding to the bits c_(i) at the output.

It is noted that the SNR estimator in the described embodiments isapplied at the input of the differential demodulator: if the SNRestimator is applied at the output of the differential demodulator thereis a greater insensitivity to the frequency offset, the disadvantagebeing the noise amplification.

In the graphs of FIGS. 11 and 12, there are shown the estimatedsignal-to-noise ratio SNRs versus the exact value SNRe over values ofΔf_(n) being 10⁻⁴ and 5·10⁻⁵ of the SNR estimator for a single carrierin accordance with the known art and the second embodiment being B=4 andL=8 and the mean square error MSE versus the value SNRe over values ofΔf_(n) being 10⁻⁴ and 5·10⁻⁵ of the SNR estimator in accordance with theknown art and the second embodiment being B=4 and L=8, respectively; theestimator in accordance with the known art is indicated as SNV whereasthe estimator in accordance with the second embodiment is indicated asRSNVS(B, L). Both graphs show the estimator in accordance with the knownart for Δf_(n)=0, indicated as BOUND.

From the values of FIGS. 11 and 12, the improvement of the RSNVSestimator performances is apparent as compared to the SNV estimator.

The used pass-band single carrier communication system of an embodimentworks at a carrier frequency of 100 kHz and has a system clock having atolerance of ±200 ppm or ±100 ppm and a sampling frequency being F=10kHz with the SNR estimator applied at the input of the differentialdemodulator.

The used pass-band multiple carrier communication system of anembodiment works at a carrier frequency of 250 kHz and has a systemclock having a tolerance of ±40 ppm or ±20 ppm and a sampling frequencybeing F=100 kHz with the SNR estimator applied at the input of thedifferential demodulator. A person skilled in the art may makemodifications, adaptations and replacements of elements with othersfunctionally equivalent to the embodiments described above so as tosatisfy contingent requirements while remaining within the scope ofprotection of the following claims. Each of the characteristicsdescribed as pertaining to a possible embodiment may be realizedindependently of the other embodiments described.

The foregoing detailed description has set forth various embodiments ofthe devices and/or processes via the use of block diagrams and examples.Insofar as such block diagrams and examples contain one or morefunctions and/or operations, it will be understood by those skilled inthe art that each function and/or operation within such block diagrams,flowcharts, or examples can be implemented, individually and/orcollectively, by a wide range of hardware, software, firmware, orvirtually any combination thereof. In one embodiment, the presentsubject matter may be implemented via Application Specific IntegratedCircuits (ASICs). In one embodiment, the present subject matter may beimplemented via one or more digital signal processors executing, forexample, instructions stored on one or more memories. However, thoseskilled in the art will recognize that the embodiments disclosed herein,in whole or in part, can be equivalently implemented in standardintegrated circuits, as one or more computer programs executed by one ormore computers (e.g., as one or more programs running on one or morecomputer systems), as one or more programs executed by on one or morecontrollers (e.g., microcontrollers) as one or more programs executed byone or more processors (e.g., microprocessors), as firmware, usingdiscrete circuitry, or as virtually any combination thereof, and thatdesigning the circuitry and/or writing the code for the software and orfirmware would be well within the skill of one of ordinary skill in theart in light of the teachings of this disclosure.

When logic is implemented as software and stored in memory, logic orinformation can be stored on any computer-readable medium for use by orin connection with any processor-related system or method. In thecontext of this disclosure, a memory is a computer-readable medium thatis an electronic, magnetic, optical, or other physical device or meansthat contains or stores a computer and/or processor program. Logicand/or the information can be embodied in any computer-readable mediumfor use by or in connection with an instruction execution system,apparatus, or device, such as a computer-based system,processor-containing system, or other system that can fetch theinstructions from the instruction execution system, apparatus, or deviceand execute the instructions associated with logic and/or information.

In the context of this specification, a “computer-readable medium” canbe any element that can store the program associated with logic and/orinformation for use by or in connection with the instruction executionsystem, apparatus, and/or device. The computer-readable medium can be,for example, but is not limited to, an electronic, magnetic, optical,electromagnetic, infrared, or semiconductor system, apparatus or device.More specific examples (a non-exhaustive list) of the computer readablemedium would include the following: a portable computer diskette(magnetic, compact flash card, secure digital, or the like), a randomaccess memory (RAM), a read-only memory (ROM), an erasable programmableread-only memory (EPROM, EEPROM, or Flash memory), a portable compactdisc read-only memory (CDROM), digital tape. Note that thecomputer-readable medium could be any suitable medium upon which theprogram associated with logic and/or information can be electronicallycaptured, via for instance optical scanning, then compiled, interpretedor otherwise processed in a suitable manner if necessary, and thenstored in memory.

The various embodiments described above can be combined to providefurther embodiments. All of the U.S. patents, U.S. patent applicationpublications, U.S. patent applications, foreign patents, foreign patentapplications and non-patent publications referred to in thisspecification and/or listed in the Application Data Sheet areincorporated herein by reference, in their entirety. Aspects of theembodiments can be modified, if necessary to employ concepts of thevarious patents, applications and publications to provide yet furtherembodiments.

These and other changes can be made to the embodiments in light of theabove-detailed description. In general, in the following claims, theterms used should not be construed to limit the claims to the specificembodiments disclosed in the specification and the claims, but should beconstrued to include all possible embodiments along with the full scopeof equivalents to which such claims are entitled. Accordingly, theclaims are not limited by the disclosure.

1. A method comprising: receiving a modulated signal, the signalcomprising a sequence of N known transmitted symbols modulated usingM-ary Differential Phase Shift Keying (M-DPSK) modulation with at leastone carrier; and estimating, using at least one processor, asignal-to-noise ratio based on a division of N samples of the receivedsignal and of the N known transmitted symbols into a number of blocks Bof a length L, with N, B and L being positive integer values with B>1and L<N.
 2. The method of claim 1 wherein the estimating thesignal-to-noise ratio based on the number of blocks B and the length Lcomprises estimating the signal-to-noise ratio based on a complexconjugate of the M-DPSK known transmitted symbols.
 3. The method ofclaim 2 wherein the estimating the signal-to-noise ratio based on thenumber of blocks B and the length L is performed according to:$\begin{matrix}{{SNR} = {{{( {1 - \frac{1}{L}} )\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}} - \frac{1}{L}} =}} \\{= {\frac{( {L - 1} ){\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}} - {L{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}}\end{matrix}$ wherein l_(b)=L·b+l, l is an index denoting a position ofa first known symbol of the sequence of length N in a packet, r_(k) is asample of the received signal at an output of a channel correspondent toa known transmitted symbol, a_(k) is the M-DPSK known transmittedsymbol, a*_(k) is a complex conjugate of the M-DPSK known transmittedsymbol and SNR indicates an estimation of the signal-to-noise ratio. 4.The method according to claim 2 wherein when the length L of the blocksB is greater than a threshold, the estimation of the signal-to-noiseratio is given by:${{SNR} = \frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}},$wherein l_(b)=L·b+l, l is an index denoting a position of a first knownsymbol of the sequence of length N in a packet, r_(k) is a sample of thereceived signal at an output of a channel correspondent to a knowntransmitted symbol, a_(k) is the M-DPSK known transmitted symbol, a*_(k)is a complex conjugate of the M-DPSK known transmitted symbol and SNRindicates an estimation of the signal-to-noise ratio.
 5. The methodaccording to claim 2 wherein$B = {{\frac{N - L}{L - O} + 1} \geq \frac{N}{L}}$ factor of consecutiveblocks having length L, and estimation of the signal-to-noise ratiobeing given by:${{SNR} = {\frac{\frac{( {L - 1} )}{B \cdot L}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}},$wherein l_(b)=L·b+l, l is an index denoting a position of a first knownsymbol of the sequence of length N in a packet, r_(k) is a sample of thereceived signal at an output of a channel correspondent to a knowntransmitted symbol, a_(k) is the M-DPSK known transmitted symbol, a*_(k)is a complex conjugate of the M-DPSK known transmitted symbol and SNRindicates an estimation of the signal-to-noise ratio.
 6. The methodaccording to claim 1, further comprising: filtering the receivedmodulated signal; and applying non-coherent type differentialdemodulation to the filtered signal after estimation of thesignal-to-noise ratio.
 7. The method according to claim 1 wherein the atleast one carrier comprises multiple carriers.
 8. An apparatus,comprising: a module configured to obtain a number B of blocks of alength L based on a division of a number N of known symbols and of anumber N of samples of a received signal at an output of a channel, withN, B and L being positive integer values, and B greater than one; and anestimator configured to estimate, based on the number of blocks B andthe length L, a signal-to-noise ratio of the received signal comprisinga sequence of the N known symbols modulated using M-ary DifferentialPhase Shift Keying (M-DPSK) modulation with at least one carrier signal.9. The apparatus of claim 8, wherein the module configured to obtain thenumber of blocks B comprises a divider configured to divide the N knownsymbols and N samples of the received signal at the output of thechannel into the number of blocks B of the length L.
 10. The apparatusof claim 8 wherein the estimator is configured to estimate thesignal-to-noise according to: $\begin{matrix}{{SNR} = {{( {1 - \frac{1}{L}} )\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}} - \frac{1}{L}}} \\{= {\frac{( {L - 1} ){\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}} - {L{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}}\end{matrix}$ wherein l_(b)=L·b+l, l is an index denoting a position ofa first known symbol of the sequence of length N in a packet, r_(k) is asample of the received signal at the output of the channel correspondentto a known transmitted symbol, a_(k) is the M-DPSK known transmittedsymbol, a*_(k) is a complex conjugate of the M-DPSK known transmittedsymbol and SNR indicates an estimation of the signal-to-noise ratio. 11.The apparatus according to claim 8 wherein if the length L of the blocksB is greater than a threshold, the estimator is configured to estimatethe signal-to-noise ratio according to${{SNR} = \frac{\frac{1}{B\;}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}},$wherein l_(b)=L·b+l, l is an index denoting a position of a first knownsymbol of the sequence of length N in a packet, r_(k) is a sample of thereceived signal at the output of the channel correspondent to a knowntransmitted symbol, a_(k) is the M-DPSK known transmitted symbol, a*_(k)is a complex conjugate of the M-DPSK known transmitted symbol and SNRindicates an estimation of the signal-to-noise ratio.
 12. The apparatusaccording to claim 8 wherein$B = {{\frac{N - L}{L - O} + 1} \geq \frac{N}{L}}$ wherein O indicatesan overlapping factor of consecutive blocks having length L, andestimation of the signal-to-noise ratio being given by:${{SNR} = {\frac{\frac{( {L - 1} )}{B \cdot L}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}},$wherein l_(b)=L·b+l, l is an index denoting a position of a first knownsymbol of the sequence of length N in a packet, r_(k) is a sample of thereceived signal at the output of the channel correspondent to a knowntransmitted symbol, a_(k) is the M-DPSK known transmitted symbol, a*_(k)is a complex conjugate of the M-DPSK known transmitted symbol and SNRindicates an estimation of the signal-to-noise ratio.
 13. The apparatusof claim 8, further comprising: a filter configured to filter thereceived signal; and a differential demodulator configured to demodulatethe received signal and to receive as an input the estimatedsignal-to-noise ratio.
 14. The apparatus of claim 8 wherein the at leastone carrier signal comprises a plurality of carrier signals.
 15. Acomputer-readable memory medium whose contents cause at least oneprocessor to perform a method, the method comprising: obtaining a numberof blocks B of a length L based on a division of a number of knownsymbols N and of N samples of a received signal at an output of achannel into the number of blocks B of length L, with B, L and Npositive integer values, and B greater than one; and estimating, basedon the number of blocks B and the length L, a signal-to-noise ratio of areceived signal comprising a sequence of the N known symbols modulatedusing M-ary Differential Phase Shift Keying (M-DPSK) modulation with atleast one carrier signal.
 16. The computer-readable memory medium ofclaim 15 wherein the method further comprises differential demodulationof the received signal.
 17. The computer-readable medium of claim 15wherein the obtaining comprises dividing the N known symbols and Nsamples of the received signal at the output of the channel into thenumber of blocks B of length L.
 18. The computer-readable medium ofclaim 15 wherein B is greater than N divided by L.
 19. A system,comprising: a differential demodulator configured to demodulate areceived signal comprising a sequence of N known symbols modulated usingM-ary Differential Phase Shift Keying (M-DPSK) modulation with at leastone carrier signal; and an estimator configured to estimate asignal-to-noise ratio of the received signal based on a division of theN known symbols and of N samples of the received signal at an output ofa channel into a number of blocks B of length L, with N, B and L beingpositive integer values, and B greater than one.
 20. The system of claim19 wherein the estimator comprises a divider configured to divide theknown symbols N and N samples of the received signal at the output ofthe channel into the number of blocks B of the length L.
 21. The systemof claim 19, further comprising a filter.
 22. The system of claim 19,further comprising a transmitter configured to transmit a signal,wherein the differential demodulator and the estimator are configured toreceive the transmitted signal.
 23. The system of claim 19 furthercomprising a transmitter configured to transmit modulated signals.
 24. Asystem comprising: means for obtaining a number of blocks B of a lengthL based on a division of a sequence of known symbols N and of N samplesof a received signal at an output of a channel into the number of blocksB; and means for estimating, based on the number of blocks B and thelength L, a signal-to-noise ratio of a received signal comprising asequence of the N known symbols modulated using M-ary Differential PhaseShift Keying (M-DPSK) modulation with at least one carrier signal.
 25. Amethod for estimating a signal-to-noise ratio for a packet transmissionand reception system of signals having a known data sequence by means ofa M-DPSK modulation with at least one carrier, said system comprisingpacket transmission of a signal with a sequence of N known symbols, withN positive integer number, said transmission comprising a M-DPSKmodulation of the signal to transmit by means of a M-PSK mapper and adifferential block, the transmission of the M-DPSK modulated signal(s(t)) through a channel having constant gain (G) over all the N symbolsand in presence of noise (w(t)) with null average, and reception of asignal (r(t)) at the output of the channel, said method comprisesestimation of a signal-to-noise ratio of the received signal with thedivision of the N known symbols (a_(k)) and of the N samples (r_(k)) ofthe signal (r(t)) at the output of the channel into B blocks of L lengthwith B and L positive integer numbers and B greater than one and whereinB is expressed by $B = {{\frac{N - L}{L - O} + 1} \geq \frac{N}{L}}$wherein O indicates an overlapping factor of consecutive blocks havinglength L and calculation of the estimation of the signal-to-noise ratioby means of an equation:${SNR} = {\frac{\frac{( {L - 1} )}{B \cdot L}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}$wherein l_(b)=b·(L−O)+l where l is an index denoting a position of afirst known symbol of the sequence of length N in the packet, r_(k) is asample of the received signal at the output of the channel correspondentto a known transmitted symbol, a_(k) is the M-DPSK modulated knowntransmitted symbol, a*_(k) is a complex conjugate of the M-DPSKmodulated known transmitted symbol and SNR indicates the estimation ofthe signal-to-noise ratio.
 26. The method according to claim 25 whereinwhen O=0 the B blocks are expressed by $B = \frac{N}{L}$ and saidestimation of the signal-to-noise ratio is given by: $\begin{matrix}{{SNR} = {{( {1 - \frac{1}{L}} )\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}} - \frac{1}{L}}} \\{= {{\frac{( {L - 1} ){\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}} - {L{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}..}}\end{matrix}$
 27. The method according to claim 25 wherein when thelength L of the blocks B is sufficient great to average the noise, saidestimation of the signal-to-noise ratio is given by:${SNR} = {\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}.}$28. The method according to claim 25 wherein said transmission andreception system is of a pass-band type and the reception is of anon-coherent type with differential demodulation, said estimation of thesignal-to-noise ratio being effectuated before the differentialdemodulation of the signal.
 29. The method according to claim 25 whereinsaid transmission and reception system is of a multiple carrier type.30. An apparatus to estimate a signal-to-noise ratio for a packettransmission and reception system of signals having a known datasequence by means of a M-DPSK modulation with at least one carrier, saidsystem comprising means for the packet transmission of a signal with asequence of N known symbols, with N positive integer number, saidtransmission means comprising a M-DPSK modulator of the signal totransmit comprising a M-PSK mapper and a differential block, said M-DPSKmodulated signal (s(t)) being adapted to pass through a channel havingconstant gain (G) over all the N symbols and in presence of noise (w(t))with null average, said system comprises means (10) for receiving asignal (r(t)) at an output of the channel, said apparatus comprisingfirst means adapted to divide the N known symbols (a_(k)) and the Nsamples (r_(k)) of the signal (r(t)) at the output of the channel into Bblocks of L length with B and L positive integer numbers and B greaterthan one and said first means (101) being adapted to overlap consecutiveblocks having length L of a factor O, said B blocks being expressed by$B = {{\frac{N - L}{L - O} + 1} \geq \frac{N}{L}}$ wherein O indicatesan overlapping factor of consecutive blocks having length L, and secondmeans adapted to calculate the estimation of the signal-to-noise ratioby means of an equation:${SNR} = {\frac{\frac{( {L - 1} )}{B \cdot L}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}$wherein −l_(b)=(L−O)·b+l where l is an index denoting a position of afirst known symbol of the sequence of length N in the packet, r_(k) is asample of the received signal at the output of the channel correspondentto a known transmitted symbol, a_(k) is the M-DPSK modulated knowntransmitted symbol, a*_(k) is a complex conjugate of the M-DPSKmodulated known transmitted symbol and SNR indicates the estimation ofthe signal-to-noise ratio.
 31. The apparatus according to claim 30wherein O=0 and said second means being adapted to effectuate theestimation of the signal-to-noise ratio by an equation: $\begin{matrix}{{SNR} = {{( {1 - \frac{1}{L}} )\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{N}{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}} - \frac{1}{L}}} \\{= {\frac{( {L - 1} ){\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\sum\limits_{k = l}^{l + N - 1}{r_{k}}^{2}} - {L{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - {\frac{1}{L}.}}}\end{matrix}$
 32. The apparatus according to claim 30 wherein when thelength L of the blocks B is sufficient great to average the noise saidsecond means are adapted to calculate the estimation of thesignal-to-noise ratio by an equation:${SNR} = {\frac{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}}.}$33. The apparatus according to claim 30 wherein said transmission andreception system is of a pass-band type, said reception means of thesignal effectuating a non-coherent reception and comprising adifferential demodulator, said estimation apparatus being adapted tocalculate the estimation of the signal-to-noise ratio of the signal atan input of the differential demodulator.
 34. The apparatus according toclaim 6 wherein said transmission and reception system is of a multiplecarrier type.
 35. A packet transmission and reception system of signalshaving a known data sequence by means of a M-DPSK modulation with atleast one carrier, said system comprising means for packet transmissionof a signal with a sequence of N known symbols, with N positive integernumber, said transmission means comprising a M-DPSK modulator of thesignal to transmit comprising a M-PSK mapper and a differential block,said M-DPSK modulated signal (s(t)) being adapted to pass through achannel having constant gain (G) over all the N symbols and in presenceof noise (w(t)) with null average, said system comprising means forreceiving a signal (r(t)) at the output of the channel which comprises adifferential demodulator, said system including an apparatus comprisingfirst means adapted to divide the N known symbols (a_(k)) and N samples(r_(k)) of the signal (r(t)) at the output of the channel into B blocksof L length with B and L positive integer numbers and B greater than oneand said first means (101) being adapted to overlap consecutive blockshaving length L of a factor O, said B blocks being expressed by$B = {{\frac{N - L}{L - O} + 1} \geq \frac{N}{L}}$ wherein O indicatesan overlapping factor of consecutive blocks having length L, and secondmeans adapted to calculate the estimation of the signal-to-noise ratioby means of an equation:${SNR} = {\frac{\frac{( {L - 1} )}{B \cdot L}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}{{\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}}^{2}}}}} - {\frac{1}{B}{\sum\limits_{b = 0}^{B - 1}{{\frac{1}{L}{\sum\limits_{k = l_{b}}^{l_{b} + L - 1}{r_{k}a_{k}^{*}}}}}^{2}}}} - \frac{1}{L}}$wherein l_(b)=(L−O)·b+l where l is an index denoting a position of afirst known symbol of the sequence of length N in the packet, r_(k) is asample of the received signal at the output of the channel correspondentto a known transmitted symbol, a_(k) is the M-DPSK modulated knowntransmitted symbol, a*_(k) is a complex conjugate of the M-DPSKmodulated known transmitted symbol and SNR indicates an estimation ofthe signal-to-noise ratio.